Question 1081768

The quadratic function has 2 real zeroes that differ by 18. Find the value of c.

f(x)= 2x^2 -24x+c

I've tried to plug in numbers but I dont get answers that differs by 18
<pre>Let zeroes (roots) be {{{matrix(1,3, r[1], and, r[2])}}}
Then: {{{matrix(1,5, sum, of, roots, "=", - b/a)}}} =====> {{{matrix(1,3, r[1] + r[2], "=", - - 24/2)}}} =====> {{{matrix(1,3, r[1] + r[2], "=", 12)}}} ------ eq (i)
Also, {{{matrix(1,3, r[1] - r[2], "=", 18)}}} ----- Given ------ eq (ii)
{{{2r[1] = 30}}} ------ Adding eqs (ii) & (i)
{{{highlight_green(matrix(1,5, r[1], "=", 30/2, or, 15))}}}

{{{15 + r[2] = 12}}} ------- Substituting 15 for {{{r[1]}}} in eq (i)
{{{highlight_green(matrix(1,5, r[2], "=", 12 - 15, or, - 3))}}}

Also, {{{matrix(1,5, Product, of, roots, "=", c/a)}}} ======> {{{matrix(1,3, r[1]r[2], "=", c/2)}}}
{{{15(- 3) = c/2}}}
{{{- 45 = c/2}}}
{{{c = - 45(2)}}} --------- Cross-multiplying
{{{highlight_green(matrix(1,3, c, "=", - 90))}}}